Square of the Sum of Two Numbers

Transcript

Square of the Sum of Two NumbersWe have an Identity Let’s do an example of this The area of a square of sidelength 60 units is 3600 sq. units (602) and that of a square of sidelength 5 units is 25 sq. units (52). Can we use this to find the area of a square of sidelength 65 units? We can split our square of length 65 into 4 parts A square of length 60 A square of length 5 Two rectangles – 5 × 60 and 60 × 5 Let’s look at it visually Thus, 652 = (60 + 5)2 = 602 + 5 × 60 + 60 × 5 + 52 = 602 + 5 × 60 + 5 × 60 + 52 = 602 + 2 × 5 × 60 + 52 = 3600 + 600 + 25 = 4225 Now, let’s answer a question = 3600 + 600 + 25 = 4225 Now, let’s answer some questions What if we write 652 as (30 + 35)2 or (52 + 13)2? Draw the figures and check the area Calculating using the formula 652 = (30 + 35)2 = 302 + 2 × 30 × 35 + 352 = 900 + 2100 + 1225 = 4225 Or 652 = (52 + 13)2 = 522 + 2 × 52 × 13 + 132 = 900 + 2100 + 1225 = 4225 We can convert 65 to a sum of any two numbers and get the same answer Example: We divide 102 into different parts, but get the same area Here, 102 = (8 + 2)2 And, 102 = (3 + 7)2 Both areas is same Now, let’s do some questions